Why won't my hp notebook turn on the light for the on button blinks But does not turn on?

In most cases your HP notebook is in "power saving" mode. Please make sure your notebook is plugged into a power source as the battery could the result of the "blinking" ON button. If the battery is low, the computer will not turn on and will stay in "sleep" mode. If this is not the case, simply press and hold your power button that is blinking for 5-10 seconds. You will see your computer turn-off. Press the power button again (*given that the steps above have been followed through) and your computer light should turn back on and remain solid.

If for some reason you find that the "ON" button light is constantly blinking, but the HP notebook is not turning on, make sure that your battery is not dead, and your power supply (the actual power cable and black power bar) is working.